Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 898626, 14 pages
doi:10.1155/2010/898626
Research Article

Optimality and Duality in Nonsmooth Multiobjective Optimization Involving V-Type I Invex Functions

Ravi P. Agarwal,1,2 I. Ahmad,1,3 Z. Husain,4 and A. Jayswal5

1Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
2Department of Mathematical Sciences, Florida Institute of Techynology, Melbourne 32901, USA
3Department of Mathematics, Aligarh Muslim University, Aligarh-202 002, India
4Department of Mathematics, Faculty of Applied Sciences, Integral University, Lucknow 226026, India
5Department of Applied Mathematics, Birla Institute of Technology, Mesra, Ranchi 835 215, India

Received 4 June 2010; Accepted 26 September 2010

Academic Editor: R. N. Mohapatra

Copyright © 2010 Ravi P. Agarwal et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A new class of generalized V-type I invex functions is introduced for nonsmooth multiobjective programming problem. Based upon these generalized invex functions, we establish sufficient optimality conditions for a feasible point to be an efficient or a weakly efficient solution. Weak, strong, and strict converse duality theorems are proved for Mond-Weir type dual program in order to relate the weakly efficient solutions of primal and dual programs.